Potato is a major global crop that has an important role to play in food security, reducing poverty and improving human nutrition. Enhanced atmospheric CO2 concentrations provide an opportunity to increase potato yields in the future, but this will only be possible if the potato crop can cope with the other consequences of climate change caused by this rise in CO2. While climate change may impact biotic stress either positively or negatively, abiotic stresses are likely to be greatly increased and become a major threat to potato production. Increasing heat, drought and salinity stress will drive the need for greater understanding of genes, traits and management techniques that allow potato to cope with these stresses. In this review, we identify some of the key physiological and molecular adaptations of potato to these stresses and propose an ideotype which should include (1) optimal stomatal regulation to balance water loss and heat stress in leaves, (2) production of metabolites and transporters to scavenge reactive oxygen species and partition toxic elements, (3) enhanced root systems to maximise water capture, (4) maintenance of tuberisation under stress conditions and (5) stress avoidance by accelerating crop development and reducing time to yield. We discuss potential ways to achieve this ideotype, emphasising the need to benefit from genetic diversity in landrace and wild material by screening for traits in combined stress environments appropriate to future agroecosystems.